Experimental Pricing As an Approach to Demand Analysis 21
Quadratic Component.-The large reduction in the error sum
of squares, accounted for by the linear component, suggested the
possibility of extending the model to form (C). That is, the
rejection of H1 directed attention to the tentative inclusion of a
quadratic component in the model. Upon the postulation of
form (C), the hypothesis to be tested became H2: B0 = 0 against
"2 : 010 0.
The regression coefficients and sum of squares for regression
resulting from the introduction of the quadratic component of
price into the model were obtained by solving
Erx Zy7x8 y7x9 -Ey7XI0
Sy7x, xgx, Exx, 2xOxl
x7xIO xx9O zX9XIO 8xlO
txixi0 x8xo0 Ex9x, o xo J
ASSR7,8,9,10 [b7 8 b bp "ld EYx7 yx8 E Yx9 'YO]
The solution gave
b7 = 2.050910
bs = 2.341879
b9 = -6.261668
blo = 2.409690
ASSR7,s,9,1o = 4.207578.
The F ratio in Table 4 indicates the significant reduction in
the remainder term when X'io was included in the model. The
outcome of the tests of H1 and H2 led to the decision that form
(C) was preferable to form (A) as a model for estimation. That
is, after price and quantity were adjusted for variation in the
categorical variables, a quadratic appeared more satisfactory
than a linear regression of the logarithm of quantity on the
logarithm of price. Stated in another way, the addition of
Xk-i-and Xj0ik-i to the model, along with associated parameters,
significantly improved the fit of the model to the data.
Distinctness of Age Regression.-The choice of form (C)
over form (A) precluded the necessity of testing the adequacy
of form (B) because of the linear property of this model. How-
ever, the particular form of the model was yet undecided, be-
cause the distinctness of age regression in relation to the quad-
ratic form remained to be examined. Form (D), of which form